Problem: Express your answer as a mixed number simplified to lowest terms. $9\dfrac{1}{10}-3\dfrac{2}{3} = {?}$
Find a common denominator for the fractions: $= {9\dfrac{3}{30}}-{3\dfrac{20}{30}}$ Convert ${9\dfrac{3}{30}}$ to ${8 + \dfrac{30}{30} + \dfrac{3}{30}}$ So the problem becomes: ${8\dfrac{33}{30}}-{3\dfrac{20}{30}}$ Separate the whole numbers from the fractional parts: $= {8} + {\dfrac{33}{30}} - {3} - {\dfrac{20}{30}}$ Bring the whole numbers together and the fractions together: $= {8} - {3} + {\dfrac{33}{30}} - {\dfrac{20}{30}}$ Subtract the whole numbers: $=5 + {\dfrac{33}{30}} - {\dfrac{20}{30}}$ Subtract the fractions: $= 5+\dfrac{13}{30}$ Combine the whole and fractional parts into a mixed number: $= 5\dfrac{13}{30}$